Variograms of Radar Reflectivity to Describe the Spatial Continuity of Alpine Precipitation

Abstract

The authors use variograms of radar reflectivity as a summary statistic to describe the spatial continuity of Alpine precipitation on mesogamma scales. First, how to obtain such variograms is discussed. Second, a set of typical variograms of Alpine precipitation is found. Third, some examples are given on how these variograms can be used to tackle several questions such as, What spatial variation of precipitation rate can be found in Alpine catchments? What difference can be expected between the measurements at two points separated by a given distance? To what accuracy can areal precipitation be estimated from point observations? Are there preferred regions for convection in Alpine precipitation? Variograms are obtained using a method-of-moments estimator together with high-resolution polar reflectivity data of well-visible regions. Depending on the application, the variogram was determined in terms of linear precipitation rate, logarithmic reflectivity, or linear reflectivity. Spatial continuity was found to vary significantly both in time and space in the various types of Alpine precipitation analyzed so far. At a separation distance of 10 km, the expected difference of reflectivity ranges from 4 dBZ (factor of 2.5 in stratiform rain or snow) to about 13 dBZ (factor of 20 in a mesoscale convective system). In a 96-h period of heavy rain in the southern European Alps, maximum variation occurred in upslope regions (frequent convection), while close to the crest of the Alps the variation was relatively weak (persistent stratiform rain). The representativeness of a point observation, which can be quantified given the variogram, therefore depends on both the time and the location within the Alps and also on the integration time (integrated rainfall maps being less variable than instantaneous ones). For a 576-km² basin and 40-min average rain, the fractional error of the basin precipitation estimated by a gauge measurement ranges from 11% (variogram of stratiform autumn rain) to 65% (variogram of a mesoscale convective system). Next steps will extend the variogram analyses to a larger space–time domain toward a climatic description of spatial continuity of Alpine precipitation.